Solidification kinetics of the unmodified aluminium-silicon flake structure

Acta metall, mater. Vol. 41, No. 8, pp. 2433-2439, 1993

0956-7151/93 $6.00+ 0.00 Copyright © 1993Pergamon Press Ltd

Printed in Great Britain.All fights reserved

SOLIDIFICATION KINETICS OF THE U N M O D I F I E D A L U M I N I U M - S I L I C O N FLAKE STRUCTURE S. KHAN 1 and R. ELLIOTT 2 IMetallurgy Division, Dr A. Q. Khan Research Laboratories, P.O. Box No. 502, Kauhta, Rawalpindi, Pakistan and 2Material Science Centre, University of Manchester, Manchester M1 7HS, England (Received 18 September 1992; in revised form 20 January 1993)

Abstraet--Aluminium-silicon eutectic alloys were directionally solidified to study the development of microstructure as a function of growth conditions. The dependencies upon growth conditions are described by the relationship of the form AT = AV°-55G -°43 and 22-3sV= BG -°6 (where A and B are constants). This is in agreement with the argument made by Toloui and Hellawell. The results are also compared with the recent model of Magnin and Kurz which showed that this model is unable to explain the growth behaviour of the unmodified AI-Si flake structure.

1. INTRODUCTION The properties of the A1-Si eutectic alloys are best exploited when these alloys are solidified directionally. This alloy is widely used due to its good castability and excellent mechanical properties. Close control over the microstructure during solidification helps to optimize its mechanical and physical properties. It is achieved by influencing the nucleation and growth behaviour of the alloy; by adding ternary elements such as Na/Sr or by solidifying the eutectic at a high growth velocity. Eutectic alloys are classed as regular and irregular [1-3]. The regular eutectic is typified by low melting entropy of the two phases. The irregular eutectic, however, contains one phase with high melting entropy, resulting in a different growth behaviour. In general the two types are known as non-faceted/non-faceted (regular) and non-faceted/faceted (irregular). Regular eutectics are associated with lamellar or rod form of microstructures. Once the nucleation has occurred growth proceed in a coupled manner with an isothermal interface. The growth process is characterized by interparticle spacing (2), growth velocity (V) and total interface undercooling (AT) which is made up of diffusional, curvature and kinetic factors. Hunt and Jackson [4] have explained the growth behaviour of the regular eutectic by the following unique relationship A T = KI V2 + K2/,~

(1)

where K~ and K2 are constants for the given alloy system. Differentiation of equation (1) leads to basic relationships on which the growth of the eutectic depends A T / x / V = 2 x / K l K2 (2) ~2V ~- K 2 / K 1

AT2ex = 2K2. ^u 41/S--L

(3) (4)

According to equation (1) the undercooling (AT) of the solid-liquid interface exhibits a characteristic minimum at critical value of lamellar spacing (2), for a given growth velocity (V). Consequently, this minimum (extremum) has been assumed to be the operative point of the system, shown in Fig. 1. The relationships established for the regular eutectic are independent of temperature gradient. The anomalous eutectics of which A1-Si is the common example, form a variety of microstructures such as broken lamellar, flake, fibrous and complex regular. The growth of the anomalous A1-Si flake structure is known to deviate from the normal pattern. Growth occurs at a non-isothermal interface and the average interflake spacing and the total interface undercooling are larger than predicted by equation (1). They are also temperature gradient dependent [5]. It was demonstrated that the growth of A1-Si flake structure [6] still lies on the AT-2 curve (growth curve), however, the operative points are at the maximum of the curve as shown in Fig. 1. Flake eutectic grown at a constant velocity exhibits a range of spacing because the growth direction of the faceting phase is defined by specific orientations and may not always lie in the heat flow direction. The flake structure is considered to grow in the following manner: as the two flakes grow together one will block the growth of the other, Fig. 2. The average spacing will then be determined by the ability of the Si to branch or to produce a new flake to fill the gap. If the branching is difficult the average spacing will approach the minimum undercooling value. It was suggested that the large undercooling found in unmodified AI-Si flake structure is thus attributed to the diffusion term K 1V2 of equation (1). A kinetic undercooling term perhaps be included in equation (1) to allow for the kinetic undercooling of the faceted Si phase. However, it is argued that this will be small compared with the diffusion term and the total undercooling [5, 7].

2433

2434

KHAN and ELLIOTT:

10v l°°m [

SOLIDIFICATION KINETICS OF FLAKE STRUCTURE

Ir . N

between 2' and 2". The spacing at branching 2b, is given by &, = ~'A (6)

Structu U

where A is the material constant. The average flake spacing that is measured experimentally is given by <~.) = '~ex-~-2br/2 = O~'ex

egular / ~ 0.1 - ~,, \ / ~X"--.~ ~"

^ . , "Solute under cooling

where ~b is a regularity constant which is close to one for normal eutectic and 2ex is the spacing at the extremum point. If the value of F is small, the equations for flake growth corresponding to equation (2) are

)(

// / 0.01

// \\

Curvature

x under cooling

\

\

I

10

A T I x / V = (~b + 1)~bx/KiK2

I

100

,t2V = d?2K2/KI

~, (l~m) Fig. I. The theoretical growth curve as predicted by HuntJackson for regular and irregular structure. The operating point for the regular structure lies close to the extreme and for the irregular structure lies close to the curve at higher 2 and AT values.

Previous growth models [8, 9] presented for an irregular eutectics are based on Hunt and Jackson's [4] hypothesis did not gain much support due to the difficulty encountered by using non-isothermal coupling condition over a small region of the interface. A recent treatment of Magnin and Kurz [10] uses an averaged non-isotbermal coupling condition over the whole interface. This results in a modified growth relationship as

AT = K~ V2 + K2/2 + F.

(7)

(5)

The factor F is introduced to compensate for the non-isothermal interface. The operative points on the growth curve is defined using a morphological criterion to characterize the branching behaviour of the faceted phase. Branching is predicted to occur

AT2 = (~b2 + 1)K2.

(8) (9) (10)

In this paper an attempt has been made to test the significance of the Magnin and Kurz theory with the experimental results of AI-Si system.

2. EXPERIMENTAL All measurements were made from the alloy of the pure constituents of Al and Si. Samples were prepared by melting 99.99% purity Al and Si under argon atmosphere. After dissolution and homogenization the molten alloy was sucked up into alumina tubes 200 mm in length and 2.5 mm inner diameter. The specimen was then positioned in the vertical Bridgrnan furnace using cool water reservoir to promote directional solidification. Solidification rate in the range of 10-1000/~m/s and a wide range of temperature gradients were used. Thermal analysis is the usual method for measuring phase transformation temperature in metals and alloys. Conventional thermal analysis measures the heat liberated resulting from both nucleation and growth processes. Interface growth temperature can be measured from discontinuities on the time-temperature trace (cooling curve) of a fine thermocouple bead inserted in the melt. Distinct arrest on the cooling curve was not possible as the temperature gradient and growth velocity range used in the present condition was not favorable. An alternative means of locating the growth temperature was adopted. A specimen containing a thermocouple was directionally solidified until the thermocouple registered a measured temperature of approximately 550°C. The whole sample was then suddenly quenched to stabilize the growth front. The temperature registered at this time was easily identified by the sharp discontinuity on the cooling

CUrve. Fig. 2. Schematic diagram of main aspect of facetednonfaceted eutectic growth: e.g. fibre ceases to grow when local spacing reaches ~ t (lower left), minor phase branches when local spacing is sufficiently large (upper left).

The solidified specimens were sectioned longitudinally and polished to examine the interface region. Knowing the distance from the thermocouple bead to the quenched interface measured on the longitudinal sections, the growth velocity and the chart speed, it is possible to calculate the distance on the time axis

KHAN

and ELLIOTT:

SOLIDIFICATION

KINETICS

of the chart recorder. This allows the location of the interface position on the cooling curve at the time of quenching. This determines the interface temperature (r,), tAT-- r ~ - r,]. The temperature gradient in the liquid during growth was measured from the cooling curve. The gradient recorded was that just ahead of the interface. The interface growth velocity was also measured from the cooling curve. It was found that the interface growth velocity is equal to the specimen pulling rate (traction rate) up to the critical velocity, above this velocity the interface growth velocity is less than the traction rate. The critical velocity was found to be 100 gm/s for the present conditions. A detail calibration and thermal characteristics of the Bridgman furnace is given elsewhere [11].

OF

FLAKE

STRUCTURE

Micrographs were taken from the transverse sections of the specimens just below the interface to measure the interflake spacing using line intercept method. 3. EXPERIMENTAL RESULTS AND DISCUSSION The variation of interface undereooling and interflake spacing as a function of interface growth velocity is shown in Fig. 3. The growth relationships obtained are of the form

AT=24V°55G-°'43 (c, mm, s) 2z3sV = 5.48

10-TG -°'6 (mm, s).

x

(a)

i0

-

-

A

L., O o

P

s ntwor

o j

o

oprosontworkO=70°c,c -

"~A

/

, . a s o o l 1 0 o c , o m

•

AE&GG

=8*C/,cm

* T & H G = 7 *C/era t

1

t

t

i

I

t

10 Growth

I ~ I 100 velocity

t

t

t

I

t

I I L I 1000

(grin/s)

(b)

• P r e s e n t w o r k G = 122 ° C / c m o P r e s e n t w o r k G = 76 *C/era z

10

x

~

• H & S G =~110 *C/cm (

--

zx E & G G=' 8 * C / c m [] T & H G = 1 3 0 " C / c m •

~

~ Z x

~

*r&

HG

=

I

I

I

7*C/cm

o

I

1 10

I

I

I

I

I I i [ 100

Growth

2435

velocity

I

t

I I I I 1000

0xm/s)

Fig. 3. (a) Undereoolings for unmodified Al~Si eutectic are plotted as a function of growth velocity for different temperature gradients. (b) Interflake Si spacings are plotted as a function of growth velocity for different temperature gradients.

(11) (12)

K H A N and ELLIOIq':

2436

1

-0

/

/

/

_

-

NLoy

--• G OG AG • G • G 0.1

~

/

/

~

x

Table 1. Phase diagram parameters and material constants used in the study [14]

/

TE real msi CO

),%/

Factor F 7 *C/cm T&H 8 *C/cm E&G 80 *C/cm T&H 76 ° C / c m Present w o r k 122 *C/cm P r e s e n t w o r k

= = = = =

I

/

SOLIDIFICATION KINETICS OF FLAKE STRUCTURE

,

J~

~J~l

0.1

~

I I Illl[

t

1 Interflak¢

I

10 spacing

(~tm)

Fig. 4. G r o w t h c u r v e s f o r flake s h o w i n g t h e d i s p l a c e m e n t o f t h e o p e r a t i v e p o i n t s f r o m the f a c t o r F o f M a g n i n a n d K u r z t h e o r y w i t h t e m p e r a t u r e g r a d i e n t a n d g r o w t h velocity.

577.2°C 7.5 K/w% 17.5 K/wt% 98.2 wt%

DE

3 × 10 9 m 2 s - I

~AI rsl O~ Osl

9 X 10 SmK 2 x 10 7mK 25 ° 85 °

fsi

0.127

P

8.9 x 10 -3

These results confirm that anomalous A1-Si flake structure requires larger undereooling and spacing for the growth than that of normal structure. These type of structures are temperature gradient dependent. This is in agreement with the work of Toloui and Hellawell [5]. However, for reasons discussed elsewhere [12] there is not a good agreement between the two results (present and T/H) with respect to the absolute

Table 2. Table of the experimental results and calculations of the Magnin and Kurz theory G = 7°C/cm (Toloui and Hellawell) V(~m/s) 2~x 2' 2" K F 2~p

ATe,p

V(ttm/s) 2©, 2' 2" K F 2~,p ATcxp

V(um/s) 2,, 2' 2" K F

/~tp ATop

V(#m/s)

,~,

28 1.16 6.26 21.65 3.46 -0.015 11.7 4.1

54 1.15 4.59 16.01 3.49 --0.012 8.6 6.1

104 205 505 0.83 0.59 0.38 3.24 2.29 1.45 11.95 1o. 1 6.42 3.69 4.37 4.43 --9.84 x 10 -3 --0.011 --7.22 x 10 -3 6.4 5.3 3.4 8.71 14.8 21.0 G = 80°C/cm (Toloui and Hellawell)

28 1.61 6.26 8.76 1.4 --0.012 5.2 2.15

54 1.15 4.59 6.65 1.45 ---0.01 3.9 3.2

104 0.83 3.42

28 1.61 6.26 16.6 2.65

54 1.15 4.59 13.2 2.88

-8.34

x 10 - 3

9.1 3.9

28

1.16

-8.06

4.59 1.53

×

7.2 5.2

54

1.15

2' 2" K F 2exp ATexp

6.26 12.1 1.92 --0.03 6.84 1.7

4.59 9.31 2.03 --0.027 5.25 2.2

V(/~m/s) 2~x 2' 2" K F

28 1.16 6.26 8.32 1.33 --0.016

2~p

4.99

54 1.15 4.59 6.51 1.42 --0.014 3.38

Ar~

1.3

i.s

10 -3

205 0.59 2.29 3.6 1.57

505 0.38 1.45 2.42 1.67

1 8.51 32.67 144.72 ---0.17 76.62 1.1

0.1 26.9 103.28 457.53 ---0.5 242.21 0.34

0.01 85.1 326.67 1447.1

1 8.51 32.67 54.55

0.1 26.9 103.28

0.01 85.1 326.63 545.47

--

172.47 --

-1.16 766.03 0.107

--8.56 x l0 -3 --6.12 x l0 -3 --4.3 x 10 -3 2,9 2.1 1.4 4.5 6.7 11.13 G = 8°C/cm (Elliott and Glenister)

--0.104 31.53 0.46

--0.21 99.68 0.15

104 205 505 0.83 0.59 0.38 3.24 2.29 1.45 10.7 9.2 6.42 3.32 4.02 4.43 - 8 . 2 7 x 10-3 - 9 . 9 4 x l0 -3 -8.2:~ x 10 -3 5.8 4.9 3.4 8.1 12.72 21.0 G = 76°C/cm (present work)

1 8.51 32.67 144..7 --0.19 76.62 1.1

0. l 26.9 103.28 457.0 --0.56 242.21 0.34

0.01 85.1 326.63 1446.9

104 205 505 0.83 0.59 0.38 3.24 2.29 1.45 7.57 5.2 3.4 2.33 2.27 2.34 --0.027 --0.018 -0.012 4.2 2.9 1.89 3. l 5.2 14.2 G = 122°C/cm (present work)

1 8.51 32.67 76.44 --42.5 0.61

0.1 26.9 103.28 241.6 --134.28 0.19

0.01 85.1 326.63 764.31 --424.7 0.06

104 0.83 3.24 5.65

1 8.51 32.67 72.2

0.1 26,9 103.28 228.2

0.01 85.1 326.63 721.8

205 0.59 2.29 4.17

!.74

1.82

--0.018 3.24 2.4

--0.015 2.38 4.7

505 0.38 1.45 3.2 2.21 --0.016 !.79 I 1.2

--

--0.35 40.35 0.58

--

--0.54 127.5 0.18

315.3 0.047

-1.16 766.03 0.107

--

-403.5 0,06

KHAN and ELLIOTT: SOLIDIFICATION KINETICS OF FLAKE STRUCTURE magnitude of the undercooling. This is apparent in Fig. 3. The importance of the Magnin and Kurz [10] theory lies in the fact that it is the only theoretical interpretation given for the irregular eutectics and considerable advancement on the Fisher and Kurz [9] treatment. Magnin and Kurz related their analysis with the result of Fe-Gr system [13]. They claimed that their model is in close agreement with the experimental results and showed that the influnence of temperature gradient is only significant below 1 #m/s. However, the measurements made in Fe-Gr system is only at one temperature gradient and consequently no experimental data have been provided in support of their theoretical prediction for normal growth rates. It will be appropriate to test Magnin and Kurz's prediction as the data available is more comprehensive and covers a wide range of temperature gradients and growth velocities. The growth curves can be calculated according to Hunt and Jackson analysis for lamellar growth using constant values defined by Grugel and Kurz [14] i.e. K] --- 1.38 × 10 -2 ks #m -2 and K 2 = 1 k/am. The growth curves was then modified according to Magnin and Kurz theory through the dependence of their parameter F and 2' on temperature gradient and growth velocity and then compared with experimental measurements for the selected growth velocities. The resultant growth curves are shown in Fig. 4. The branching criterion defined by Magnin and Kurz is in between 2' and 2". Hence the values of 2e~, 2', 2" and F factor can be calculated using system parameter, given in Table 1, of AI-Si system for velocities of 28, 54, 104, 205 and 505/am/s and three lower velocities such as 1, 0.1 and 0.0l/am/s. Calculations were obtained for temperature gradient of 7°C/cm and 80°C/ cm (value used by Toloui and Hellawell), 8°C/cm (Elliott and Glenister) and 76°C/cm and 122°C/cm (present results). The values calculated from these data, given in Table 2, for F show that the Magnin and Kurz analysis predicts very little deviation from the Hunt and Jackson theory. The deviation has seen to occur only at low velocities which is outside the range of flake growth in the A1-Si system. The operative points can be located on the growth curves by using branching criterion defined by Magnin and Kurz model. This suggest that the operative growth points should lie in between 2ext and 2branch and that branching should lie between 2' and 2" such that '~branch = •'K

2437

determine average spacing is 3.4. So the average spacing is given by 2(2 ) = 2+xt+ 2'K

(14)

K = 4.43

(15)

This is within the limits predicted by Magnin and Kurz theory for A1-Si alloys. As this value is considered to be a material constant by Magnin and Kurz analysis it is possible to calculate the predicted operative spacing for other velocities and temperature gradient by using equation (14). The results obtained from these calculations are shown in Fig. 5(a). It is clear from this figure that a temperature gradient dependence of the operative growth points (through 2') is only predicted for the velocity below 10/am/s.

(a)

10

--

INI ~o

o

/

1 -

0.1 -- e G = 8 ° C • G = 76 °C/era • , = ,22 *C/cm 0.01 0.0,

~.~,0.0,~../

I

I

l

1

0.,

,

,0

,00

(b)

\ 10--

0., .

/--

/

~

/

~ 2 1

8_°c_ -

(13)

where K is the material constant lying between 1 and x/1 + 2/cos 0 gives the value of 4.9 for A1-Si system. It is now necessary to calculate the value for K. This is only possible using experimental results. As the deviation from Hunt and Jackson analysis is predicted to occur at low growth velocity it seems reasonable to select a high growth velocity results at low temperature gradient for determining K. The selected growth velocity is 505/am/s at 8°C/cm, the experimentally

0.01 0.01

+ 0+1

I 1

I 10

+) [ 100

Interparticle spacing (ptm) Fig. 5. (a) Showing the movement of operative growth points due to changing temperature gradient and growth velocity as predicted by Magnin and Kurz theory. (b) Showing the displacement of operative growth points from the growth curve due to the factor F combined with the displacement of operative points as shown in (a).

2438

KHAN and ELLIOTT: SOLIDIFICATIONKINETICS OF FLAKE STRUCTURE

I(a)

/

!

-

,0

Z

o., p o o : 7 . c

/,, o--~o~,<=

O.O1/

0.01

I

I

0.1

0~ 10 / .-. :~ / "~ e)

1~ /

0.1

/

10 /

\/ I

100

/

'~?J ~

~x

/

//~, ~ ' ~\

1 ~J

*with

Fig. 7.

XO / / / 505,,./ X 28 / / ~ , ~ , /

"| 1-- o G ~7~C / tx G=80*C/cm

/ 0.01 / 0.01

I

1

i~b) x

V

~-

i x~~~,~jx\ \ x /

~O.lyi \~ XO/"

~_~.'l [ ~ '~ 0.01-Rr ', I I t , 0.1 1I 10 100 lnterparticle spacing (p.m)

Fig. 6. (a,b) Analysis of Toloui and Hellawell's results as shown for present study in Fig. 5(a) and (b). To complete the theoretical prediction of growth behaviour it is necessary to include the influence of temperature gradient and growth velocity on the F parameter. This is shown in Fig. 5(b) and again it is negligible at growth velocities higher than 10/~m/s. Just below this velocity (1/~m/s) it is significant for G ffi 122°C/cm but small for 8°C/era. Hence, the theory predicts that the operative growth points for temperature gradient of 8°C/era lies on the line that is parallel to a line joining the extremum points for the velocities examined in the present work. The operative points for higher gradients are predicted to lie at the same position for growth velocities in excess of 10/tm/s. When the velocity falls below 10/~m/s the operative growth points are predicted to move towards the extremum position as the temperature gradient increases at constant velocity and as the growth velocity decreases at constant temperature gradient. The above consideration was repeated for Toloui and Hellawell results and similar behaviour

was observed i.e. the temperature gradient is only significant at low growth velocity, Fig. 6(a) and (b). From the previous and present measurements, it is concluded that the effect of temperature gradient is significant at much higher growth velocities. Magnin and Kurz have modified the growth relationships by adding the parameter ~b called regularity factor in order to explain the growth behavior of AI-Si eutectic. It has been shown [11] that this parameter ~ is decreasing with increasing temperature gradient and increasing with increasing growth velocity, Fig. 7. The parameter ~ can be used to describe the magnitude of the undercooling and flake spacing but fails to explain the influence of temperature gradient. The influence of temperature gradient is related to the sohite diffusion problem which exist with Si phase due to its anisotropic growth. The difference in freezing rate and concentration gradient ahead of the interface requires a large driving force. As the temperature gradient increases the diffusion problem is markedly reduced. This effect decreases the undercooling [12, 15]. The measurements made during the flake growth of AI-Si alloy suggest that the Magnin and Kurz analysis does not predict the temperature gradient dependence of spacing and undercooling and that the deviation predicted to occur at low growth velocities are also observed at higher growth velocities. 4. CONCLUSION The results of the unmodified AI-Si flake structure clearly suggest that influence of temperature gradient is very significant. This confirm the early postulate of Toloui and Hellawell. The Magnin and Kurz theory of flake growth does not explain the influence of temperature gradient. The deviation which is predicted to occur at low growth velocities was also observed at higher velocities. The factor F is only significant at velocities below 1/am/s with all temperature gradients which is outside the range of flake growth and above this range its contribution to total undercooling is negligible. Acknowledgements--This work was performedin Material Science Centre, Universityof Manchester. The authors are

KHAN and ELLIOTT:

SOLIDIFICATION KINETICS OF FLAKE STRUCTURE

thankful to Professor F. R. Sale for the provision of laboratory facilities and to the Ministry of Science and Technology, Government of Pakistan for funding this project. The authors are also thankful to Dr F. H. Hashmi and Dr A. Q. Khan for their support and useful comments. Thanks are due to Dr Anwar-ul-Haq for reviewing this paper critically. REFERENCES

1. J. D. Hunt and K. A. Jackson, Trans. metall. Soc. A.LM.E. 236, 834 (1966). 2. R. Elliott, Int. Metal Rev. 11219, 161 (1977). 3. R. Elliott, Eutectic Solidification Processing. Butterworth Monographs in Materials (1983). 4. J. D. Hunt and K. A. Jackson, Trans. metall. Soc. A.LM.E. 236, 1129 (1966).

2439

5. B. Toloui and A. Hellawell, Acta metall. 23, 565 (1976). 6. L. M. Hogan and H. Song, Metal. Trans. 18A, 707 (1987). 7. H. A. H. Steen and A. Hellawell, Acta metall. 22, 528 (1975). 8. T. Sato and Y. Sayama, J. Cryst. Growth 22, 259 (1974). 9. D. J. Fisher and W. Kurz, Acta metall. 28, 777 (1980). 10. P. Magnin and W. Kurz, Acta metall. 35, 1119 (1987). 11. S. Khan, Ph.D. thesis, Univ. of Manchester (1990). 12. R. Elliott and S. M. D. Glenister, Acta metall. 7,8, 1489 (1980). 13. H. Jhons and W. Kurz, Z. Metallk. 72, 259 (1981). 14. R. Grugel and W. Kurz, Metall. Trans. 18A, I137 (1987). 15. S. Khan, Conf. Proc. 2ml lnt. Syrup. on Advance Material, Pakistan, Islamabad (1991).